using Parent in integer rings instead of ParentWithGens

[fchapoton]

Let's try to get rid of the last direct inheritance to ParentWithGens.

(not quite the last one, see #37158 )

There remains many indirect inheritance, mostly through Ring, Algebra, CommutativeRing and their subclasses. This is a step towards cleaning and simplifying the old coercion framework.

The present changes is close to the heart of sage, so appropriate timings should be checked.

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[github-actions]

Documentation preview for this PR (built with commit 04a196a; changes) is ready! 🎉

[kwankyu]

The present changes is close to the heart of sage, so appropriate timings should be checked.

What timings are necessary? Would you be explicit? Did you do the timings?

[tscrim]

I think coercions and conversions with common objects (finite fields, constant polynomials, rational numbers, etc.) would be good. Although I wouldn't expect really any changes in the timings...

[fchapoton]

I ran the tests of the rings folder and the time taken seemed not to change significantly. Not done scientifically..

[kwankyu]

I got, where m is a 1000*1000 matrix of integer entries,

Before this PR:

sage: m = load('m')
sage: timeit('m^3+m^2+m')
5 loops, best of 3: 1.14 s per loop
sage: timeit('1/3*m')
5 loops, best of 3: 447 ms per loop

After this PR:

sage: m = load('m')
sage: timeit('m^3+m^2+m')
5 loops, best of 3: 1.14 s per loop
sage: timeit('1/3*m')
5 loops, best of 3: 444 ms per loop

Perhaps not enough scientific either, but I don't perceive any performance regression.

[kwankyu]

LGTM